Add the cannellini beans, sun-dried tomatoes, garlic, balsamic, and a good pinch of salt to the bowl of a food processor. Process for about a minute until relatively smooth (some small pieces of tomato are fine), scraping down the sides of the bowl a few times if necessary. With the processor running, slowly add the olive oil and process until well incorporated. Add the water one tablespoon at a time until the spread is smooth and spreadable. Season with extra salt and freshly ground black pepper to taste. Briefly set aside.
Heat the olive oil in a large skillet over high heat. When the oil is hot and shimmering (but not smoking!), add the zucchini, summer squash, a large pinch of salt, and crushed red pepper. Cook for about 4 minutes, shaking the pan occasionally, or until the squash is just tender and browned in spots. Transfer to a bowl and cover with foil to keep warm while you cook the eggs.
Poach or fry the eggs, depending on your preference.
While the eggs are cooking, toast (or grill!) the bread.
Assembly the toasts: Spread each piece of toast with a thick layer of sun-dried tomato white bean spread. Top with cooked squash and an egg. Garnish with chives and extra salt and fresh ground pepper if you like, and serve immediately.